Continuity

[granite silo]

I have to show the continuity of the following function (see pic).
But I don't know at which point should I check the continuity.
Can anyone help, please?

[sweet fjord]

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[reef coral]

each piece is a polynomial hence continuous, so you just have to check continuity on the unit circle

[azure socket]

You need to check on the boundary between pieces: x^2 + y^2 = 1.

[granite silo]

how did u get tht?

[reef coral]

looking at it

the function is split into pieces inside the unit disc and outside

inside the disc it's x^2 and outside the disc it's 2x^2+y^2-1

[granite silo]

so I have to study the continuity at the x,y such tht |(x, y)|=1 ?

[reef coral]

yes

[granite silo]

I got it thx